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The sum-connectivity index of a graph G is defined as the sum of weights 1 / d (u) + d (v) over all edges u v of G , where d (u) and d (v) are the degrees of the vertices u and v in G , respectively. A graph G is called quasi-tree, if there exists u ∈ V (G) such that G − u is a tree. In the paper, we give a sharp lower bound on the sum-connectivity index of quasi-tree graphs. [ABSTRACT FROM AUTHOR]

The forgotten topological index of a graph , denoted by F () , is defined as the sum of weights d (u) 2 + d (v) 2 overall edges u v of , where d (u) denotes the degree of a vertex u. The graph is called a quasi-unicyclic graph if there exists a vertex v ∈ () such that − v is a connected graph with a unique cycle. In this paper, we give sharp upper and lower bounds for the F-index (forgotten topological index) of the quasi-unicyclic graphs. [ABSTRACT FROM AUTHOR]